In TV systems, video scaling is often required when the native resolution of an incoming video frame does not fit the display resolution. Without loss of generality, assume the scaling ratio is L/M and the greatest common divisor gcd(L,M)=1. A conventional scaling system 100 as shown in FIG. 1 is generally used to scale an input signal x(k) with an arbitrary rational scaling ratio. In that system, the input signal x(k) is up-sampled by L in an up-sampler 102, filtered by an interpolation filter 104 with frequency response HL,M, and then down-sampled in the down-sampler 106 by M. Such process can be implemented using a polyphase structure. Using such a system, a two dimensional video frame can be first scaled in the horizontal direction with one scaling ratio and then scaled in the vertical direction with another scaling ratio, or first scaled in the vertical direction with one scaling ratio and then scaled in the horizontal direction with another scaling ratio.
In the video scaling system of FIG. 1, the up-sampling expands the time scale by a factor of L and inserts L−1 zeros between each sample of x(k), to obtain the new sequence u(k). In the frequency domain, the up-sampling introduces image components at frequency 2πl/L, 1≦l≦L−1. Therefore, in order to prevent artifacts, u(k) has to be filtered by a low-pass filter with cutoff frequency π/L. On the other hand, the down-sampling takes every Mth sample of v(k) to obtain the scaled sequence y(k). However, such down-sampling generally results in aliasing.
In order to prevent aliasing, the sequence v(k) should be filtered prior to down-sampling with a low-pass filter that has a cutoff frequency π/M. The cascade of two low-pass filters with cutoff frequencies π/L and π/M is equivalent to a single low-pass interpolation filter HL,M with a cutoff frequency min(π/L,π/M). Therefore, the frequency characteristics of the interpolation filter HL,M depend on the values of L and M.
Because the interpolation filter HL,M is a low-pass filter, the scaled video lacks in high frequency components, whereby the scaled video is often blurred and not as sharp as the original input video sequence.